few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Topic options: 
A. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
B. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
C. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
D. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
E. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
F. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
G. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
K. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.


Thought: This set of problems asks students to reason with equations, specifically linear equations, such as the one shown in the table in Problem 1.
Answer: F

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001392

8
options: Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Narrative
The purpose of this activity is for students to consider two different equations that represent the same story problem. Put Together, Result Unknown problems help students make sense of the commutative property because the two parts can be combined in different orders. This property, as well as the associative property, is referred to as “add in any order” to students. Students contextualize the problem and see that each number represents a specific object’s quantity, no matter which order it is presented, and connect these quantities to written symbols (MP2). Students will work more with the “add in any order” property in future lessons.
Representation: Access for Perception.
Students may benefit from hearing the instructions read aloud more than once.
Supports accessibility for: Language, Attention
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
“We just solved a problem about pet fish. What else do you know about pets?”
30 seconds: quiet think time
1 minute: partner discussion
If needed ask, “What kinds of pets are there?”
Activity
Read the task statement.
3 minutes: independent work time
2 minutes: partner discussion
Monitor for a student who uses objects or drawings to show that each equation matches the story.
Student Facing
Tyler and Clare want to know how many pets they have together.
Tyler has 2 turtles.
Clare has 4 dogs.
Tyler wrote the equation
\(4 + 2= \boxed{6}\)
.
Clare wrote the equation
\(2 + 4 = \boxed{6}\)
.
Do both equations match the story?
Why or why not?
Show your thinking using drawings, numbers, or words.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
If students explain that both equations match the story using only numbers, consider asking:
"How do you know that both equations match the story?"
"How could you use connecting cubes to show that they both match?"
Activity Synthesis
Invite previously identified students to share.
“How does their work show us that Tyler’s equation matches the story?”
“How does their work show us that Clare’s equation matches the story?”


correct_option_index: 8